A conventional composite heating apparatus of this type is commercially produced in which the high frequency and resistance heating are operated separately, or the resistance heating is switched automatically to heating by high frequency energy. In either type, the cooking effect obtained by simultaneous dielectric heating in which the food is heated from within and resistance heating in which the food is heated from the outside cannot be expected. Even if there would be available a composite heating apparatus capable of dielectric heating and resistance heating simultaneously, simultaneous operation of a high frequency heating apparatus of the electric capacity of, say, 1.2 KW and a resistance heating apparatus of 1.2 KW would result in a current of about 24 A flowing in an ordinary home supplied with a source voltage of 100 V, thus posing the problem that such an apparatus cannot be used due to power consumption limitations in areas having unfavorable power supply situations. Such an apparatus requires a power supply and power equipment of a large capacity, and is difficult to commercialize. Further, the simultaneous operation of both large output heaters is not desirable from the viewpoint of cooking effects and energy saving.